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Question

The length of normal to the curve x=a(θ+sin θ), y=a(1cos θ) at θ=π2 is .

A
2(a|
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B
2(a|
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C
(a|2
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D
(a|2
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Solution

The correct option is B 2(a|
Here,
dxdθ=a(1+cos θ) and dydθ=a(sin θ)or, dydx=dy/dθdx/dθ=a(sin θ)a(1+cos θ)or, (dydx)θ=π/2=sin π/21+cos π/2=1Length of normal is ((y|1+(dydx)2}θ=π/2=(a(1cos π2)1+12=2(a|.

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